pat_azel = uv2azelpat(pat_uv,u,v) expresses
the antenna radiation pattern pat_azel in azimuth/elevation
angle coordinates instead of u/v space coordinates. pat_uv samples
the pattern at u angles in u and v angles
in v. The pat_azel matrix
uses a default grid that covers azimuth values from –90 to
90 degrees and elevation values from –90 to 90 degrees. In
this grid, pat_azel is uniformly sampled with
a step size of 1 for azimuth and elevation. The function interpolates
to estimate the response of the antenna at a given direction.

pat_azel = uv2azelpat(pat_uv,u,v,az,el) uses
vectors az and el to specify
the grid at which to sample pat_azel. To avoid
interpolation errors, az should cover the range
[–90, 90] and el should cover the range
[–90, 90].

[pat_azel,az,el]
= uv2azelpat(___) returns vectors containing
the azimuth and elevation angles at which pat_azel samples
the pattern, using any of the input arguments in the previous syntaxes.

Antenna radiation pattern in u/v form,
specified as a Q-by-P matrix. pat_uv samples
the 3-D magnitude pattern in decibels in terms of u and v coordinates.
P is the length of the u vector and Q is the
length of the v vector.

Azimuth angles at which pat_azel samples
the pattern, specified as a vector of length L. Each azimuth angle
is in degrees, between –90 and 90. Such azimuth angles are
in the hemisphere for which u and v are
defined.

Antenna radiation pattern in azimuth/elevation form, returned
as an M-by-L matrix. pat_azel samples the 3-D
magnitude pattern in decibels, in terms of azimuth and elevation angles.
L is the length of the az vector, and M is the
length of the el vector.

The φ angle is the angle from the positive y-axis
toward the positive z-axis, to the vector's
orthogonal projection onto the yz plane. The φ
angle is between 0 and 360 degrees. The θ angle is the angle
from the x-axis toward the yz plane,
to the vector itself. The θ angle is between 0 and 180 degrees.

The figure illustrates φ and θ for a vector that
appears as a green solid line. The coordinate system is relative to
the center of a uniform linear array, whose elements appear as blue
circles.

The coordinate transformations between φ/θ and az/el are
described by the following equations

The azimuth angle is
the angle from the positive x-axis toward the positive y-axis,
to the vector's orthogonal projection onto the xy plane.
The azimuth angle is between –180 and 180 degrees. The elevation
angle is the angle from the vector's orthogonal
projection onto the xy plane toward the positive z-axis,
to the vector. The elevation angle is between –90 and 90 degrees.
These definitions assume the boresight direction is the positive x-axis.

Note:
The elevation angle is sometimes defined in the literature as
the angle a vector makes with the positive z-axis.
The MATLAB^{®} and Phased Array System Toolbox™ products do not
use this definition.

This figure illustrates the azimuth angle and elevation angle
for a vector that appears as a green solid line. The coordinate system
is relative to the center of a uniform linear array, whose elements
appear as blue circles.